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  • 1. Balkan, Andrew
    et al.
    Kaijser, Sten
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Hardy spaces for the strip2007In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 333, no 1, p. 347-364Article in journal (Refereed)
    Abstract [en]

    In this paper we shall study Hardy spaces of analytic functions in a strip S. Our main result is on one hand an intrinsic characterization of the spaces and on the second that polynomials are dense. We also present an orthogonal (in H-2(S)) basis of polynomials.

  • 2.
    Bartoszek, Krzysztof
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Bartoszek, Wojciech
    Gdansk Univ Technol, Dept Probabil & Biomath, Ul Narutowicza 11-12, PL-80233 Gdansk, Poland..
    A Noether theorem for stochastic operators on Schatten classes2017In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 452, no 2, p. 1395-1412Article in journal (Refereed)
    Abstract [en]

    We show that a stochastic (Markov) operator S acting on a Schatten class C-1 satisfies the Noether condition (i.e. S' (A) = A and S' (A(2)) = A(2), where A is an element of C-infinity is a Hermitian and bounded operator on a fixed separable and complex Hilbert space (H, <.,.>)), if and only if S(E-A(G)XEA(G)) = E-A (G)S(X)E-A (G) for any state X is an element of C-1 and all Borel sets G subset of R, where E-A (G) denotes the orthogonal projection coming from the spectral resolution A = integral(sigma(A)) zE(A)(dz). Similar results are obtained for stochastic one-parameter continuous semigroups.

  • 3. Betancor, Jorge J.
    et al.
    Castro, Alejandro J.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Farina, Juan C.
    Rodriguez-Mesa, L.
    Solutions of Weinstein equations representable by Bessel Poisson integrals of BMO functions2015In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 431, no 1, p. 440-470Article in journal (Refereed)
    Abstract [en]

    We consider the Weinstein type equation L(lambda)u = 0 on (0, infinity) X (0, infinity), where L-lambda= delta(2)(t) + delta-lambda(lambda-1)/x(2), In this paper we characterize the solutions of L(lambda)u = = 0 on (0, infinity) x (0, infinity) representable by Bessel-Poisson integrals of BMO-functions as the ones satisfying certain Carleson properties.

  • 4.
    Ekström, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Convexity of the optimal stopping boundary for the American put option2004In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 299, no 1, p. 147-156Article in journal (Refereed)
    Abstract [en]

    We show that the optimal stopping boundary for the American put option is convex in the standard Black–Scholes model. The methods are adapted from ice-melting problems and rely upon studying the behavior of level curves of solutions to certain parabolic differential equations.

  • 5.
    Ekström, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematics I -V.
    Tysk, Johan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematics I -V.
    Convexity preserving jump-diffusion models for option pricing2007In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 330, no 1, p. 715-728Article in journal (Refereed)
    Abstract [en]

    We investigate which jump-diffusion models are convexity preserving. The study of convexity preserving models is motivated by monotonicity results for such models in the volatility and in the jump parameters. We give a necessary condition for convexity to be preserved in several-dimensional jump-diffusion models. This necessary condition is then used to show that, within a large class of possible models, the only convexity preserving models are the ones with linear coefficients.

  • 6.
    Ekström, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Tysk, Johan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    The Black-Scholes equation in stochastic volatility models2010In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 368, no 2, p. 498-507Article in journal (Refereed)
    Abstract [en]

    We study the Black-Scholes equation in stochastic volatility models. In particular, we show that the option price is the unique classical solution to a parabolic differential equation with a certain boundary behaviour for vanishing values of the volatility. If the boundary is attainable, then this boundary behaviour serves as a boundary condition and guarantees uniqueness in appropriate function spaces. On the other hand, if the boundary is non-attainable, then the boundary behaviour is not needed to guarantee uniqueness, but is nevertheless very useful for instance from a numerical perspective.

  • 7.
    Gaidashev, Denis
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    On analytic perturbations of a family of Feigenbaum-like equations2011In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 374, no 2, p. 355-373Article in journal (Refereed)
    Abstract [en]

    We prove existence of solutions (0, A.) of a family of Feigenbaum-like equations phi(x) = 1+is an element of/lambda phi(phi(lambda x))- is an element of x + tau(x), (0.1) where epsilon is a small real number and tau is analytic and small on some complex neighborhood of (-1, 1) and real-valued on R. The family (0.1) appears in the context of period-doubling renormalization for area-preserving maps (cf. Gaidashev and Koch (preprint) 171). Our proof is a development of ideas of H. Epstein (cf. Epstein (1986) PI, Epstein (1988) In Epstein (1989) [4]) adopted to deal with some significant complications that arise from the presence of the terms -epsilon X + tau(x) in Eq. (0.1). The method relies on a construction of novel a-priori bounds for unimodal functions which turn out to be very tight. We also obtain good bounds on the scaling parameter lambda. A byproduct of the method is a new proof of the existence of a Feigenbaum-Coullet-Tresser function.

  • 8. Garoni, Carlo
    et al.
    Manni, Carla
    Serra-Capizzano, Stefano
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Sesana, Debora
    Speleers, Hendrik
    Lusin theorem, GLT sequences and matrix computations: An application to the spectral analysis of PDE discretization matrices2017In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 446, p. 365-382Article in journal (Refereed)
  • 9.
    Gut, Allan
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
    Stadtmüller, Ulrich
    Laws of the single logarithm for delayed sums of random fields II2008In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 346, no 2, p. 403-414Article in journal (Refereed)
    Abstract [en]

    In an earlier paper we extended Lai's (1974) law of the single logarithm for delayed sums to a class of delayed sums of random fields. In this paper we allow for more general windows.

  • 10.
    Gut, Allan
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
    Stadtmüller, Ulrich
    On the Hsu-Robbins-Erdős-Spitzer-Baum-Katz theorem for random fields2012In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 387, no 1, p. 447-463Article in journal (Refereed)
    Abstract [en]

    The by now classical results on convergence rates in the law of large numbers involving the sums Sigma(infinity)(n=1) n(alpha r-2)P(vertical bar S(n)vertical bar > n(alpha)epsilon), where r > 0, alpha > 1/2, such that alpha r >= 1 has been extended to the case alpha = 1/2 by adding additional logarithms. All of this has been generalized to random fields by the first named author in [A. Gut, Marcinkiewicz laws and convergence rates in the law of large numbers for random variables with multidimensional indices, Ann. Probab. 6 (1978) 469-482; A. Gut, Convergence rates for probabilities of moderate deviations for sums of random variables with multidimensional indices, Ann. Probab. 8 (1980) 298-313]. The purpose of the present paper is to treat the case when the alpha's differ in the different directions of the field, as well as mixed cases with some alpha's equal to 1/2 with added logarithms and/or iterated ones.

  • 11.
    Gut, Allan
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
    Steinebach, Josef
    Convergence rates in precise asymptotics2012In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 390, no 1, p. 1-14Article in journal (Refereed)
    Abstract [en]

    Let Xi, X-2, ... be i.i.d. random variables with partial sums S-n, n >= 1. The now classical Baum-Katz theorem provides necessary and sufficient moment conditions for the convergence of Sigma(infinity)(n=1) n(r/p-2) P(vertical bar S-n vertical bar >= epsilon n(1/p)) for fixed epsilon > 0. An equally classical paper by Heyde in 1975 initiated what is now called precise asymptotics, namely asymptotics for the same sum (for the case r = 2 and p = 1) when, instead, epsilon SE arrow 0. In this paper we extend a result due to Klesov (1994), in which he determined the convergence rate in Heyde's theorem.

  • 12. Hed, Lisa
    et al.
    Persson, Håkan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Plurisubharmonic approximation and boundary values of plurisubharmonic functions2014In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 413, no 2, p. 700-714Article in journal (Refereed)
    Abstract [en]

    We study the problem of approximating plurisubharmonic functions on a bounded domain Omega by continuous plurisubharmonic functions defined on neighborhoods of (Omega) over bar. It turns out that this problem can be linked to the problem of solving a Dirichlet type problem for functions plurisubharmonic on the compact set (Omega) over bar in the sense of Poletsky. A stronger notion of hyperconvexity is introduced to fully utilize this connection, and we show that for this class of domains the duality between the two problems is perfect. In this setting, we give a characterization of plurisubharmonic boundary values, and prove some theorems regarding the approximation of plurisubharmonic functions.

  • 13.
    Janson, Svante
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Konstantopoulos, Takis
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Yuan, Linglong
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory. Johannes Gutenberg Univ Mainz, Inst Math, Staudingerweg 9, D-55099 Mainz, Germany..
    On a representation theorem for finitely exchangeable random vectors2016In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 442, no 2, p. 703-714Article in journal (Refereed)
    Abstract [en]

    A random vector X = (X1, ... ,X-n) with the X-i taking values in an arbitrary measurable space (S, Sp) is exchangeable if its law is the same as that of (X-sigma(1), ... ,X-sigma(n)) for any permutation a. We give an alternative and shorter proof of the representation result (Jaynes [6] and Kerns and Szekely [9]) stating that the law of X is a mixture of product probability measures with respect to a signed mixing measure. The result is "finitistic" in nature meaning that it is a matter of linear algebra for finite S. The passing from finite S to an arbitrary one may pose some measure-theoretic difficulties which are avoided by our proof. The mixing signed measure is not unique (examples are given), but we pay more attention to the one constructed in the proof ("canonical mixing measure") by pointing out some of its characteristics. The mixing measure is, in general, defined on the space of probability measures on S; but for S =, one can choose a mixing measure on R-n.

  • 14.
    Klimek, Maciej
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Matsuura, Masaya
    Department of Mathematics, Ehime University, Matsuyama, Japan.
    Okabe, Yasunori
    Department of Mathematics, Meiji University, Kawasaki, Japan.
    Stochastic flows and finite block frames2008In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 342, no 2, p. 816-829Article in journal (Refereed)
    Abstract [en]

    With the aim of understanding the mathematical structure of the fluctuation–dissipation theorem in non-equilibrium statistical physics and then constructing a mathematical principle in the modeling problem for time series analysis, we have developed the theory of KM2O-Langevin equations for discrete time stochastic processes. In this paper, as a new method for model analysis in the theory of KM2O-Langevin equations, we show that block frames provide a natural mathematical language for dealing with minimum norm expansions of multi-dimensional stochastic processes which do not necessarily satisfy stationarity and non-degeneracy conditions.

  • 15.
    Melgaard, M
    Cardiff University.
    Spectral properties at a threshold for two-channel Hamiltonians I. Abstract theory2001In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 256, no 1, p. 281-303Article in journal (Refereed)
    Abstract [en]

    Spectral properties at thresholds are investigated for two-channel Hamiltonians in various, mostly fairly "singular" settings. In an abstract framework we deduce asymptotic expansions of the resolvent as the spectral parameter tends to a threshold. The results are based on given asymptotic expansions of the component Hamiltonians. Applications to scattering theory are given in a companion paper. (C) 2001 Academic Press.

  • 16.
    Melgaard, M
    Cardiff University.
    Spectral properties at a threshold for two-channel Hamiltonians II. Applications to scattering theory2001In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 256, no 2, p. 568-586Article in journal (Refereed)
    Abstract [en]

    Spectral properties and scattering theory in the low-energy limit are investigated for two-channel Hamiltonians with Schrodinger operators as component Hamiltonians. In various, mostly fairly "singular" settings asymptotic expansions of the resolvent are deduced as the spectral parameter tends to the threshold zero. Furthermore scattering theory for pairs of two-channel Hamiltonians is established. As an application of the expansions of the resolvent, asymptotic expansions of the scattering matrix are derived as the energy parameter tends to the threshold zero. (C) 2001 Academic Press.

  • 17. Michalowski, Nicholas
    et al.
    Rule, David
    Staubach, Wolfgang
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Multilinear pseudo differential operators beyond Calderon-Zygmund theory2014In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 414, no 1, p. 149-165Article in journal (Refereed)
    Abstract [en]

    We consider two types of multilinear pseudodifferential operators. First, we prove the boundedness of multilinear pseudodifferential operators with symbols which are only measurable in the spatial variables in Lebesgue spaces. These results generalise earlier work of the present authors concerning linear pseudo-pseudodifferential operators. Secondly, we investigate the boundedness of bilinear pseudodifferential operators with symbols in the Hormander S-p,delta(m) classes. These results are new in the case p < 1, that is, outwith the scope of multilinear Calderon-Zygmund theory. (C) 2014 Elsevier Inc. All rights reserved.

  • 18. Muhamadiev, Èrgash
    et al.
    Nazarov, Murtazo
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Optimal bounds for a Lagrange interpolation inequality for piecewise linear continuous finite elements in two space dimensions2015In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 423, p. 940-955Article in journal (Refereed)
  • 19.
    Musonda, John
    et al.
    Malardalen Univ, Div Appl Math, Box 883, S-72123 Vasteras, Sweden..
    Kaijser, Sten
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Three systems of orthogonal polynomials and L-2-boundedness of two associated operators2018In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 459, no 1, p. 464-475Article in journal (Refereed)
    Abstract [en]

    In this paper, we describe three systems of orthogonal polynomials belonging to the class of Meixner-Pollaczek polynomials, and establish some useful connections between them in terms of three basic operators that are related to them. Furthermore, we investigate boundedness properties of two other operators, both as convolution operators in the translation invariant case where we use Fourier transforms and for the weights related to the relevant orthogonal polynomials. We consider only the most important but also simplest case of L-2-spaces. However, in subsequent papers, we intend to extend the study to L-p-spaces (1 < p < infinity).

  • 20.
    Nyström, Kaj
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    On the behaviour near expiry for multi-dimensional American options2008In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 339, p. 644-654Article in journal (Refereed)
  • 21. Okpoti, C.
    et al.
    Persson, Lars-Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Sinnamon, G.
    An equivalence theorem for some integral conditions with general measures related to Hardy´s inequality2007In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 326, no 1, p. 398-413Article in journal (Refereed)
    Abstract [en]

    It is proved that, besides the usual Muckenhoupt condition, there exist four different scales of conditions for characterizing the Hardy type inequality with general measures for the case 1<pq<∞. In fact, an even more general equivalence theorem of independent interest is proved and discussed.

  • 22.
    Oleynik, Anna
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Ponosov, Arcady
    Wyller, John
    On the properties of nonlinear nonlocal operators arising in neural field models2013In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 398, no 1, p. 335-351Article in journal (Refereed)
    Abstract [en]

    We study the existence and continuous dependence of stationary solutions of the one-population Wilson-Cowan model on the steepness of the firing rate functions. We investigate the properties of the nonlinear nonlocal operators which arise when formulating the stationary one-population Wilson-Cowan model as a fixed point problem. The theory is used to study the existence and continuous dependence of localized stationary solutions of this model on the steepness of the firing rate functions. The present work generalizes and complements previously obtained results as we relax on the assumptions that the firing rate functions are given by smoothed Heaviside functions.

  • 23.
    Rodriguez-Lopez, Salvador
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Staubach, Wolfgang
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Some endpoint estimates for bilinear paraproducts and applications2015In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 421, no 2, p. 1021-1041Article in journal (Refereed)
    Abstract [en]

    In this paper we establish the boundedness of bilinear paraproducts on local BMO spaces. As applications, we also investigate the boundedness of bilinear Fourier integral operators and bilinear Coifman-Meyer multipliers on these spaces and also obtain a certain end-point result concerning Kato Ponce type estimates.

  • 24. Schindler, Ian
    et al.
    Tintarev, Kyril
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Semilinear equations on fractal blowups2009In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 352, no 1, p. 57-64Article in journal (Refereed)
    Abstract [en]

    The paper concerns existence of a ground state for a nonlinear scalar field equation on a blowup fractal, where imbedding of the energy space into L-P is not compact. In absence of invariant transformations involved in conventional concentration-compactness argument, the paper develops convergence reasoning based on the fractal's self-similarity.

  • 25.
    Schippers, Eric
    et al.
    Univ Manitoba, Dept Math, Canada..
    Staubach, Wolfgang
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Harmonic reflection in quasicircles and well-posedness of a Riemann-Hilbert problem on quasidisks2017In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 448, no 2, p. 864-884Article in journal (Refereed)
    Abstract [en]

    A complex harmonic function of finite Dirichlet energy on a Jordan domain has boundary values in a certain conformally invariant sense, by a construction of H. Osborn. We call the set of such boundary values the Douglas-Osborn space. One may then attempt to solve the Dirichlet problem on the complement for these boundary values. This defines a reflection of harmonic functions. We show that quasicircles are precisely those Jordan curves for which this reflection is defined and bounded. We then use a limiting Cauchy integral along level curves of Green's function to show that the Plemelj-Sokhotski jump formula holds on quasicircles with boundary data in the Douglas-Osborn space. This enables us to prove the well-posedness of a Riemann-Hilbert problem with boundary data in the Douglas Osborn space on quasicircles.

  • 26.
    Sjöberg, Anders
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    On the Korteweg–de Vries equation: Existence and uniqueness1970In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 29, p. 569-579Article in journal (Refereed)
1 - 26 of 26
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